[bcg1]

This is not a technical solution, but you could release your code under AGPL and take code contributions.

By doing this, you are essentially telling the world that not only do they need to trust you, but that you are willing to make yourself legally culpable if you surreptitiously run different code on your servers (ie., you would be violating the copyright terms of your contributors whose code is licensed under AGPL and of which your application is a derivative).

It would be nice to have a technical solution as well, I'm not discounting any of the other suggestions here. Just saying that adding a legal dimension could help counterbalance the possibility that a technical protection could be defeated.